The Real Number System

Friday, February 4, 2011 - 12:00 - 12:50

Today, we finished topics from Section 7.4 with a discussion of the real number system. Some basic notes:

C - complex numbers (e.g., 2+3i), also called "imaginary numbers"
R - real numbers (all decimals, fractions, natural numbers and integers)
Q - rational numbers (a/b where a and b are integers, b not zero) The Q here stands for "quotient."
Z - integers (e.g., -2, 3, 120, -110, 0). The Z is German for "zahl" = "number".
N - natural numbers (the counting numbers: 1, 2, 3, 4,...)
W - the whole numbers (the natural numbers and zero)

We also discussed some properties of irrational numbers. Here's a weird fact (the proof is left to advanced analysis courses in mathematics): There are infinitely many more irrational numbers than there are rational numbers. But, our minds are wired to think in rational and natural numbers. I asked the class to name as many irrational numbers as they could name, and we came up with: pi, sqrt(2), and e. In fact, these are great examples, but they are the only ones we could name... and we could name infinitely many rational numbers: 1, 2, 3, 4, 5,... and on and on!

Here's a link to a page about irrational numbers.

© 2011 Jason B. Hill. All Rights Reserved.